APR Calculator
Determine the true annual cost of your loan including fees.
The total amount you are borrowing.
The base rate advertised by the lender.
Duration of the loan in years.
Origination fees, points, and other costs.
Real APR (Annual Percentage Rate):
0.00%
Monthly Payment (Principal & Interest):
$0.00
Total Interest Paid:
$0.00
Total Cost (Principal + Interest + Fees):
$0.00
Understanding Annual Percentage Rate (APR)
The Annual Percentage Rate (APR) is a broader measure of the cost of borrowing money than the nominal interest rate. While the interest rate reflects the cost of borrowing the principal amount, the APR includes the interest rate plus other costs associated with the loan, such as broker fees, discount points, and closing costs. This calculator helps you uncover the true cost of a loan by factoring in these upfront expenses.
Why APR is Different from Interest Rate
When lenders advertise loans, they often highlight the nominal interest rate because it looks lower. However, if a loan requires you to pay significant upfront fees, your effective rate of return on the money you actually receive is lower, or conversely, the cost of the money is higher. The APR standardizes this metric, allowing you to compare loans with different fee structures apples-to-apples.
How APR is Calculated
Calculating APR is complex because it requires solving for the interest rate in an annuity formula where the present value is the "Net Amount Financed" rather than the gross loan amount. The logic follows these steps:
- Determine Monthly Payment: First, the monthly payment is calculated using the standard loan amount and nominal interest rate.
- Calculate Net Proceeds: Subtract total fees (origination, points, closing costs) from the Loan Amount. This is the actual cash value the borrower receives.
- Solve for APR: Using the Net Proceeds as the Present Value and the Monthly Payment calculated in step 1, we use an iterative numerical method (like Newton-Raphson) to find the new interest rate that amortizes the Net Proceeds over the loan term to zero. This new rate, annualized, is the APR.
Key Inputs Explained
- Loan Amount: The principal sum you intend to borrow.
- Nominal Interest Rate: The annual rate charged by the lender, excluding fees.
- Loan Term: The lifespan of the loan, usually expressed in years (e.g., 15 or 30 years for mortgages).
- Total Fees & Costs: The sum of all upfront charges required to obtain the loan. This is the crucial variable that drives the APR higher than the nominal rate.
Interpreting Your Results
If the APR is significantly higher than the interest rate, it indicates high upfront fees. When comparing two loans, the one with the lower APR is generally the cheaper option over the full life of the loan. However, if you plan to sell the asset or refinance quickly, a loan with a higher APR but lower upfront costs might actually be beneficial, as the APR assumes you hold the loan for the full term.